Methods for producing patterns by means of an electron beam exposure device have been known in the art for a long time. The required pattern is broken down into small elementary figures and projected onto a layer of photosensitive dye. After development of the resist the pattern should be imaged in the resist as accurately as possible. The exposure of a resist with an electron beam of a certain shape (Gaussian profile beam or shaped beam or multi-pixel beam) produces a dose distribution in the resist which does not correspond to the dose profile for the electron beam. The reason for that is the scattering of the electrons by the atoms or molecules of the resist and the substrate. This is called the proximity effect.
There a short range effect (ca. 20 nm . . . 40 nm, forward-scattering) and a considerably longer range effect (ca. 5,000 nm . . . 30,000 nm, back-scattering) occur. Said effects result in a widening of the electron beam (“smearing of the dose distribution”) and a mutual interference of the dose distributions of different elementary figures, so that in the end, if all desired elementary figures are exposed with the same dose and unchanged geometry, the dose distribution produced in the resist is so distorted that the structures produced in the resist do not have the CDs of the desired pattern. Usually the pattern produced becomes useless for the desired purpose. To correct this effect, a mathematical model of the proximity effect must first be developed.
It is widely accepted that the effect can be described as a superposition of two Gaussian functions (Formula (1)), wherein alpha and beta represent the forward- and back-scattering ranges and eta describes the ratio of one effect to the other.
Formula 1
      f    ⁡          (      r      )        =            1              π        ⁡                  (                      1            +            η                    )                      ⁢          (                                    1                          α              2                                ⁢                      ⅇ                                          r                2                                            α                2                                                    +                              η                          β              2                                ⁢                      ⅇ                          -                                                r                  2                                                  β                  2                                                                        )      
This function is also called the Point Spread Function (PSF). To utilize it in a not-yet-determined correction method, the parameters a and b have to be determined. For this purpose, exposures with predefined test patterns are carried out using various methods and the CDs of the figures are measured on the test patterns in the resist. However, the results of these measurements include not only the PSF but also other influences which are thus included in the calibration.
Said influences are, in particular, the so-called beam blur caused by Coulomb interaction between the electrons and lens aberrations in the electromagnetic imaging systems, as well as effects during exposure and development caused by the chemical properties of the resist. For this reason, the function calibrated over the entire process will be hereinafter called “Process Proximity Function” (PPF). In defining the PPF it may be necessary to superpose more than two Gaussian functions.
The resulting dose distribution can then be calculated as the result of the convolution operation of the PPF with the pattern itself. As can be easily seen, said function is radially symmetric, position-independent and monotonically decreasing towards the outside.
To ensure that the resist pattern produced by electron beam lithography is usable, the proximity effect, which is unavoidable (for physical reasons), must be corrected. The usual procedure in an electron beam exposure device that supports dose control of the electron beam is to cut the figures of the pattern into smaller figures and to calculate individual doses for said smaller figures until it is ensured that the figures of the pattern have the desired CD after completion of the entire process (exposure and development of the resist).
A method with dose and geometry correction that is suitable for any pattern is described in DE 4317899 C2 and implemented in the known and commercially available PROXECCO software. This method is based on the mathematical technique of “deconvolution by suitable Fourier transforms”, hereinafter referred to in brief as “deconvolution”. A further method is disclosed in DE 198 18440 C2.
All correction methods in accordance with the state of the art suffer from some problems. The proximity correction methods known to us work satisfactorily only as long as the CDs of the figures in the pattern are greater than approximately 1.3 times the alpha parameter (cf. Seo) of the PPF. The current state of the art in semiconductor technology, however, requires CDs of about 35 nm, and by 2016 even 22 nm will be required (ITRS Roadmap). Lithography processes which are currently available and applicable in semiconductor production have (in particular due to the resists belonging to the respective process) an alpha parameter of about 25 . . . 30 nm, i.e. direct exposure is only possible down to about 38 . . . 45 nm. A number of suggestions for further improving the imaging quality in existing processes are known in the art, cf. for example US-PS 2008/0067446 A1. All of these suggestions for improving the correction begin with modifying the correction algorithm based on “deconvolution” and have so far not succeeded in improving quality significantly.